Abstract
A generalized solution of a mixed problem for the wave equation is constructed under minimal conditions on the right side of the equation. The solution is represented as a series from the Fourier method, and its sum is found. The form of a generalized solution of a mixed problem for an inhomogeneous telegraph equation is given.
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ACKNOWLEDGMENTS
The author is grateful to Khromov and Kornev for helpful discussions of the results of this work and for valuable suggestions concerning the study of problem (1)–(3).
Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2022-284.
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Translated by I. Ruzanova
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Lomov, I.S. Generalized Solution of a Mixed Problem for the Wave Equation with a Nonsmooth Right-Hand Side. Dokl. Math. 109, 121–124 (2024). https://doi.org/10.1134/S1064562424701898
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DOI: https://doi.org/10.1134/S1064562424701898